SAT Math Practice Question #1633 (Medium (620)) | Test Citadel
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SAT Math Difficulty: Medium (620)

Digital SAT Math Practice Question #1633

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In the system of equations below, \(k\) is a constant: \(\begin{cases} 4x - 6y = 15 \\ kx - 9y = 28 \end{cases}\) If the system has no solutions, what is the value of \(k\)?
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No solution = same slope: k/4 = (-9)/(-6) = 1.5 -> k = 6.

Masterclass Solution & Distractor Trap Analysis

A linear system has no solution when the lines are parallel (slopes are equal) with different y-intercepts. The ratio of coefficients of x and y must match: \(\frac{k}{4} = \frac{-9}{-6} = \frac{3}{2}\). Therefore, \(k = 4 \times \frac{3}{2...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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